The author uses data from 1946 to 2000 to compare the ability of three regression
models to predict aggregate stock market returns from dividend yields (DY) and
two other financial ratios. He uses a base model, a model that unconditionally
adjusts for the interdependence of DY and market returns, and a model that makes
a conditional adjustment. The author finds that the base model has some
predictive power, which is eliminated by the unconditional adjustment. The
conditional adjustment reduces the base-model coefficient, but it reduces the
standard error more, causing an increase in the predictive power of DY.
Predictive models based on earnings-to-price and book-to-market ratios are not
as strong as the models based on DY, but the author finds the effect of the
unconditional and conditional adjustment to be generally the same as in the DY
models.
Earlier studies have used dividend yields (DY), earnings-to-price ratios (E/Ps), and
book-to-market ratios (B/Ms) as independent variables in regression models used to
predict aggregate stock market returns. The basic model is that returns are a function
of a ratio calculated from a previous period. For the regression to be
“predictive,” the ratio must be known before the dependent variable (market
returns) is calculated. This model violates the regression assumption of independence
between the dependent variable and the independent variable (the ratio). Higher returns
are caused by price increases, which reduce each of these ratios because price is in the
denominator.
One method to correct this problem is the inclusion of a second equation that models the
autocorrelation of the independent variable. Because the error terms of the base model
and the autocorrelation model are correlated, the coefficient of the base model can be
adjusted to correct for the interdependent relationship between the ratio and market
returns. Previous research indicates that this unconditional adjustment to the base
model tends to eliminate any predictive relationship between ratios and stock market
returns.
The author proposes an alternative to the unconditional adjustment. Because the
autoregressive coefficient cannot be greater than 1.0, he suggests limiting the
adjustment to the base model by setting the autoregressive coefficient to about 1.0 (or
0.9999). This method provides for the largest adjustment to the base model given the
characteristics of the autoregressive relationship and minimizes the value of the
adjusted coefficient. If the adjusted coefficient is significant given this restrictive
adjustment, it is also significant if the autoregressive relationship is less than 1.0,
which would have made the adjustment to the base model less. This method is referred to
as the conditional adjustment to the base model.
The author uses CRSP price and dividend data from January 1946 to December 2000 for the
NYSE Index. He uses Compustat financial data from 1963 to 2000 to calculate B/Ms and
E/Ps. The author calculates returns on a monthly basis and converts all values to
natural logs. He estimates four return variations: nominal value-weighted returns
(VWNY), nominal equal-weighted returns (EWNY), excess VWNY, and excess EWNY. The author
adjusts the excess returns for the one-month U.S. T-bill rate.
When the author examines the results based on the total sample using the DY as the
predictive variable, he finds a smaller decrease in the adjusted coefficient under the
conditional adjustment procedure than under the unconditional adjustment procedure. The
standard error under the conditional adjustment procedure is also reduced, thereby
increasing the predictive power of the conditional adjustment model relative to the
unadjusted base model. These results hold for all return definitions.
The author divides the data into two subperiods: 1946–1972 and 1973–2000. He
finds that DY predicted excess market returns in the first subperiod and in all four
return definitions in the second subperiod. Under these shortened subperiods, the author
finds that the unconditional adjustment did not do very well but that the conditional
adjustment improved the predictive power of the models. To test the impact of the
unusual market conditions in the last half of the 1990s, he separates the data into two
subperiods: 1946–1994 versus 1995–2000. Again, the author finds that the
unconditional adjustment performed poorly but that the conditional adjustment improved
the predictive powers of the models.
Results based on B/M and E/P were not as promising as the DY results. Based on the total
sample, the B/M models were not able to predict either nominal or excess value-weighted
returns. Results for nominal and excess equal-weighted returns were similar to DY
results, with the unconditional adjustment reducing the predictive power of B/M and the
conditional adjustment improving it. Results based on E/P indicated a predictive
relationship to nominal market returns, but not for excess returns. The author finds
that the impact of the 1995–2000 data was less on conditional-adjusted estimates
than on unconditional-adjusted estimates for both the B/M and E/P models.